Assume that one stock follows the process dS/S = dt + dZ (20.44) Another stock follows the

Question:

Assume that one stock follows the process
dS/S = αdt + σdZ (20.44)
Another stock follows the process
dQ/Q = αQdt + σdZ + dq1+ dq2 (20.45)
(The σdZ terms for S and Q are identical.) Neither stock pays dividends. dq1 and dq2 are both Poisson jump processes with Poisson parameters λ1 and λ2. Conditional on either jump occurring, the percentage change in the stock price is Y1 − 1 or Y2 − 1. Consider the two stock price processes, equations (20.44) and (20.45).
a. If there were no jump terms (i.e., λ1 = λ2 = 0), what would be the relation between α and αQ?
b. Suppose there is just one jump term (λ2 = 0) and that Y1> 1. In words, what does it mean to have Y1> 1? What can you say about the relation between α and αQ?
c. Write an expression for αQ when both jump terms are nonzero. Explain intuitively why αQ might be greater or less than α.